Population dynamics with a stable efficient equilibrium

We propose a game-theoretic dynamics of a population of replicating individuals. It consists of two parts: the standard replicator one and a migration between two different habitats. We consider symmetric two-player games with two evolutionarily stable strategies: the efficient one in which the population is in a state with a maximal payoff and the risk-dominant one where players are averse to risk. We show that for a large range of parameters of our dynamics, even if the initial conditions in both habitats are in the basin of attraction of the risk-dominant equilibrium (with respect to the standard replication dynamics without migration), in the long run most individuals play the efficient strategy.     

Population dynamics in a spin-glass model of chemical evolution

Summary We introduce a simple model describing the evolution of a population of information-carrying macromolecules. We discuss the asymptotic dependence of the variability of the population on different parameters, representing the severity or the fluctuations of the environment. We show the existence of a transition separating a neutralist evolutionary regime from a trapped one. We investigate the dependence of the evolutionary behavior of the population on the correlation properties of the fitness landscape.     

Population dynamics of scrapie in a sheep flock.

A detailed analysis of an outbreak of natural scrapie in a flock of Cheviot sheep is described. A total of 137 cases was reported over 13 years among 1307 sheep born into the flock. The epidemiology of scrapie can only be understood with reference to sheep demography, the population genetics of susceptibility to scrapie, pathogenesis during a long incubation period, and the rate of transmission (by both vertical and horizontal routes), all of which interact in complex ways. A mathematical model incorporating these features is described, parameter values and model inputs are derived from available information from the flock and from independent sources, and model outputs are compared with the field data. The model is able to reproduce key features of the outbreak, including its long duration and the ages of cases. The analysis supports earlier work suggesting that many infected sheep do not survive to show clinical signs, that most cases arise through horizontal transmission, and that there is strong selection against susceptible genotypes. However, important aspects of scrapie epidemiology remain poorly understood, including the possible role of carrier genotypes and of an environmental reservoir of infectivity, and the mechanisms maintaining alleles giving susceptibility to scrapie in the sheep population.     

Population dynamics of host-parasite interactions in a cockroach-oxyuroid system

Host-parasite interactions of an urban cockroach, Blattella germanica , and its oxyuroid parasite, Blatticola blattae , were investigated. Life history data of host and parasites were collected under laboratory conditions. These data were used to model the effect of the parasite on the population dynamics of the host in order to understand the parasite's impact on the host population. The aggregation of parasites within a host was under-dispersed. Hosts normally were found to be infected with only one male and one female and rarely two or three. However, the primary sex ratio after hatching was 1.1 (males/females). Female parasite longevity equalled the life span of its host. B. blattae had a significant impact on the survival rate of the cockroach larvae and their time to reach maturity, but no effect on the survival rate of the adults. Infected host females produced fewer first oothecae than uninfected ones. Using the population parameters a simple model was developed to estimate the parasite's effect on the population dynamics of its host. According to the model the parasite suppresses the cockroach populations by ca 11%. Hence, the effect of the parasite does not appear strong enough to be used as a biological control agent by itself.     

Population dynamics of zooxanthellae during a bacterial bleaching event

Each summer 80–90% of the colonies of Oculina patagonica undergo bleaching off the Mediterranean coast of Israel. To investigate fluctuations through a yearly bleaching cycle, monthly measurements of zooxanthella density, mitotic index and chlorophyll-a concentration were conducted. Results showed (1) a significant negative correlation between sea surface temperature (SST) and zooxanthella density; (2) both significantly lower zooxanthella mitotic index and higher chlorophyll-a per zooxanthella content during the bleaching season compared with the non-bleaching period; (3) prior to bleaching, a lag between the peak of zooxanthella density and chlorophyll-a concentration followed by a similar lag during recovery. Zooxanthella density declined significantly between March and May while chlorophyll-a concentration peaked in April, and then declined. Zooxanthella density increased significantly in November while chlorophyll-a concentration increased significantly in January. We conclude that during bacterial bleaching events, zooxanthellae are severely damaged. However, by the time of the following bleaching event the coral tissues regain their “normal” (pre-bleaching) zooxanthella population density.     

Population dynamics of epiphytic orchids in a metapopulation context

Background and Aims

Populations of many epiphytes show a patchy distribution where clusters of plants growing on individual trees are spatially separated and may thus function as metapopulations. Seed dispersal is necessary to (re)colonize unoccupied habitats, and to transfer seeds from high- to low-competition patches. Increasing dispersal distances, however, reduces local fecundity and the probability that seeds will find a safe site outside the original patch. Thus, there is a conflict between seed survival and colonization.

Methods

Populations of three epiphytic orchids were monitored over three years in a Mexican humid montane forest and analysed with spatially averaged and with spatially explicit matrix metapopulation models. In the latter, population dynamics at the scale of the subpopulations (epiphytes on individual host trees) are based on detailed stage-structured observations of transition probabilities and trees are connected by a dispersal function.

Key Results

Population growth rates differed among trees and years. While ignoring these differences, and averaging the population matrices over trees, yields negative population growth, metapopulation models predict stable or growing populations because the trees that support growing subpopulations determine the growth of the metapopulation. Stochastic models which account for the differences among years differed only marginally from deterministic models. Population growth rates were significantly lower, and extinctions of local patches more frequent in models where higher dispersal results in reduced local fecundity compared with hypothetical models where this is not the case. The difference between the two models increased with increasing mean dispersal distance. Though recolonization events increased with dispersal distance, this could not compensate the losses due to reduced local fecundity.

Conclusions

For epiphytes, metapopulation models are useful to capture processes beyond the level of the single host tree, but local processes are equally important to understand epiphyte population dynamics.     

Underwater fertilization dynamics of marine green algae

We studied the fertilization dynamics of marine green algae with both analytical methods and numerical simulations. In this study, we focused on a new factor, gametic investment per unit volume of the space in which gametes searched for their partners, and compared the numbers of zygotes formed at lower investments with those at higher investments. As a function of the gametic investment for various anisogamy ratios, we found there was generally a crossover region for each series where, for gametic investments larger than the crossover region, isogamy prevailed with the highest number of zygotes formed, while for gametic investments smaller than the crossover region, anisogamy dominated. These results may explain both the stable maintenance of isogamy in shallow water and the distribution of anisogamous species in deep water, since in shallow water the gametic investments typically exceed this crossover region and vice versa. Comparisons of field data from marine green algae are consistent with this hypothesis. Also, we showed that the cost of sex was approximately twofold in zygote formation when comparing isogamous species with mating types to those without mating types.     

Population dynamics of gene transfer

Horizontal transfer of nucleic acid sequences is a widespread process of genetic change in bacterial populations, one taking on a variety of specific forms. A model capturing some of the general features of this process is formulated. Two major subsidiary variants of this model are analyzed. The first lacks competition between cells. In this case, the transferred genetic element can approach fixation asymptotically if cells bearing it are viable, but not otherwise. The second variant of the proposed model has competition. This gives rise to complex dynamical possibilities, but never fixation of the transferred genetic element. It is argued that the evolutionary transition from gene transfer polymorphism to obligatory genetic exchange, and thus the origin of sex, requires either population dynamics which are not subject to growth rate density-dependence or cell-dependence on transferred genetic elements, although such dependence does not require that the element be beneficial.     

Population dynamics of obligate cooperators

Obligate cooperative breeding species demonstrate a high rate of group extinction, which may be due to the existence of a critical number of helpers below which the group cannot subsist. Through a simple model, we study the population dynamics of obligate cooperative breeding species, taking into account the existence of a lower threshold below which the instantaneous growth rate becomes negative. The model successively incorporates (i) a distinction between species that need helpers for reproduction, survival or both, (ii) the existence of a migration rate accounting for dispersal, and (iii) stochastic mortality to simulate the effects of random catastrophic events. Our results suggest that the need for a minimum number of helpers increases the risk of extinction for obligate cooperative breeding species. The constraint imposed by this threshold is higher when helpers are needed for reproduction only or for both reproduction and survival. By driving them below this lower threshold, stochastic mortality of lower amplitude and/or lower frequency than for non-cooperative breeders may be sufficient to cause the extinction of obligate cooperative breeding groups. Migration may have a buffering effect only for groups where immigration is higher than emigration; otherwise (when immigrants from nearby groups are not available) it lowers the difference between actual group size and critical threshold, thereby constituting a higher constraint.     

Population dynamics of gyrinid beetles

Summary Survival chances have been estimated for populations of the waterbeetle Gyrinus marinus Gyll. from capture-recapture sequences in 1974–1978. The average weekly survival chance is estimated as 0.9247 in spring, decreasing to 0.7701 in autumn; males survive longer than females. Survival shows little variation in time or space (variation coefficient V<0.1). Survival chance did not significantly decrease with age. Freshly emerged tenerals apparently have a lower survival chance than older beetles. The survival chance during hibernation (October–April) is about 0.33, with a greater variation between years (V=0.7) than between populations (V=0.4).Communication N⁰ 301 of the Biological Station, Wijster     

Population dynamics of stored-product mites

Summary Population fluctuation patterns were determined during 1959–70 in wheat bulks in 2 granaries typical of those used on Manitoba farms for 7 kinds of mites. The patterns were bradly similar in the 2 granaries. Outbreaks of all mites except Tarsonemus granarius and Aëroglyphus robustus were unaffected by the prolonged storage of grain; those of Acarus siro and Cheyletus eruditus occurred in unusually high numbers periodically every 2–5 years, whereas Glycyphagus destructor and Androlaelaps casalis were present in relatively low numbers from the first year of storage. A rise in T. granarius population corresponded with grain age and the succession of microfloral species. Tydeid mites occurred periodically.Pricipal component analyses of up to 26 variates including various fungal species on one grain bulk ecosystem provided a kaleidoscopic view of interrelations and dynamics of acarine populations in the grain bulks. The combination of correlated variates of which mites are a part, varied from year to year.Four factors that regulate acarine numbers, particularly those of A. siro and its natural predator C. eruditus, were identified. These are: (i) basic determinants (moisture, temperature, food, and the intrinsic rate of increase of the species); (ii) the main regulator (temperature); (iii) influencers (seed cracks, microflora, dockage, etc.); and (iv) seasonal and cyclic regulators (seasonality in temperature and several density-dependent factors). Generalized diagrams of prey-predator interactions and multivariate interrelations of each kind of mite are presented.Contribution no. 568 from Research Station, Agriculture Canada, Winnipeg, Canada. Invitation paper presented by the first author at the Joint Annual Meeting of the Entomological Societies of America, Canada, and Quebec, Montreal, Quebec, on 26 November 1972     

Gene network dynamics controlling keratinocyte migration

Translation of large‐scale data into a coherent model that allows one to simulate, predict and control cellular behavior is far from being resolved. Assuming that long‐term cellular behavior is reflected in the gene expression kinetics, we infer a dynamic gene regulatory network from time‐series measurements of DNA microarray data of hepatocyte growth factor‐induced migration of primary human keratinocytes. Transferring the obtained interactions to the level of signaling pathways, we predict in silico and verify in vitro the necessary and sufficient time‐ordered events that control migration. We show that pulse‐like activation of the proto‐oncogene receptor Met triggers a responsive state, whereas time sequential activation of EGF‐R is required to initiate and maintain migration. Context information for enhancing, delaying or stopping migration is provided by the activity of the protein kinase A signaling pathway. Our study reveals the complex orchestration of multiple pathways controlling cell migration.     

Evolutionary dynamics of genes controlling floral development

Advances in the understanding of floral developmental genetics in model species such as Arabidopsis continue to provide an important foundation for comparative studies in other flowering plants. In particular, floral organ identity genes are the focus of many projects that are addressing both ancient and recent evolutionary questions. Expanded analyses of the evolution of these gene lineages have highlighted the dynamic nature of the gene birth-and-death process, and may have significant implications for the evolution of genetic pathways. Crucial functional studies of floral organ identity genes in diverse taxa are allowing the first real insight into the conservation of gene function, while findings on the genetic control of organ elaboration offer to open up new avenues for investigation. Taken together, these trends show that the field of floral developmental evolution continues to make significant progress towards elucidating the processes that have shaped the evolution of flower development and morphology.